Final answer:
The coupon rate for the bond issued by Johns Inc. can be determined by setting up the present value equation for the bond's price and its cash flows and solving for the annual coupon payment. This amount is then divided by the bond's par value to arrive at the coupon rate per annum.
Step-by-step explanation:
The student is asking how to calculate the coupon rate per annum (p.a.) for Johns Inc.'s 10-year semi-annual fixed coupon bond, given the bond's price, par value, and yield to maturity (YTM). To compute the coupon rate, we need to know the total annual coupon payment, which we will then divide by the bond's par value ($1,000) to get the coupon rate. Since the bond pays semi-annually, there are two periods per year. The bond is issued at $1,232.58 with a yield to maturity (YTM) of 5% p.a. Knowing that YTM represents the expected return on a bond if held to maturity, we can set up the following equation where C is the annual coupon payment:
Price = (C/2) / (1 + YTM/2) + (C/2) / (1 + YTM/2)^2 + ... + (C/2 + Par Value) / (1 + YTM/2)^(2*Years)
Using a financial calculator or appropriate software, we input the following: N = 20 periods (10 years times 2, because of semi-annual payments), PV = -$1,232.58 (negative since it's an outflow), FV = $1,000, PMT = C/2 (which we're solving for), I/Y = 2.5% (because the YTM is 5% divided by 2 for semi-annual periods), and compute for PMT. Once we have the value for PMT, we can double it to get the total annual coupon payment (C) and then divide by the par value to obtain the coupon rate.